Subgroups — C₂²×C₂₃⋊C₁₆ #13092829

Order 1472.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃⋊C₁₆	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₂₃	C₄	1	3	yes	—
5	C₂×C₈×C₂₃	C₂²	1	3	yes	—
6	C₂₃⋊C₁₆	C₂²	1	4	yes	direct product factor
7	C₂³×C₂₃	C₈	1	1	yes	characteristic
8	C₂×C₄×C₂₃	C₈	1	3	yes	—
9	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
10	C₈×C₂₃	C₂×C₄	1	3	yes	—
11	C₈×C₂₃	C₂³	1	1	yes	characteristic
12	C₂²×C₂₃	C₁₆	1	4	yes	complemented
13	C₂²×C₂₃	C₂×C₈	1	3	yes	—
14	C₄×C₂₃	C₂×C₈	1	3	yes	—
15	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
16	C₂²×C₁₆	—	23	1	no	maximal, Sylow
17	C₂×C₂₃	C₂×C₁₆	1	6	yes	complemented
18	C₂×C₂₃	C₂²×C₈	1	1	yes	characteristic
19	C₂²×C₈	D₂₃	1	1	yes	characteristic
20	C₂×C₁₆	—	23	6	no	—
21	C₂₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₄	Dic₂₃	1	1	yes	characteristic
23	C₂×C₈	Dic₂₃	1	3	yes	—
24	C₂×C₈	C₂×D₂₃	1	3	yes	—
25	C₁₆	—	23	4	no	—
26	C₂³	C₂₃⋊C₈	1	1	yes	characteristic
27	C₂×C₄	C₂₃⋊C₈	1	3	yes	—
28	C₂×C₄	C₂×Dic₂₃	1	3	yes	—
29	C₈	C₂×Dic₂₃	1	3	yes	—
30	C₈	C₂²×D₂₃	1	1	yes	characteristic
31	C₂²	C₂₃⋊C₁₆	1	4	yes	direct product factor
32	C₂²	C₂×C₂₃⋊C₈	1	3	yes	—
33	C₄	C₂×C₂₃⋊C₈	1	3	yes	—
34	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
35	C₂	C₂×C₂₃⋊C₁₆	1	6	yes	direct product factor
36	C₂	C₂²×C₂₃⋊C₈	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.